Pour the cream into a large bowl and set in the egg yolks, cheese, flour, garlic and oregano to make a smooth batter. Season with freshly ground black pepper.
Heat enough oil in a deep pan for deep-frying. When hot enough the oil should be 160-180 °C (325-350°F); a piece of bread dropped in the oil will sizzle and become golden brown in 30 seconds. Dip the squid rings and tentacles into the batter, one at a time and put into the oil.
Fry for 2-3 minutes until golden brown. Drain on kitchen paper and serve immediately, sprinkled with salt.